Rotation of digital images

Abstract

The image is divided into regions of a given number of pixels. The original image is scaled down by a given factor. Each region of pixels is then enlarged in order to overlap its neighboring region. The enlarged regions are then sequentially written down in a scaled down version, in overlapped relationship, with each region oriented a given degree with respect to its neighboring region. The end result is a rotated image that has the same size as the original image with no gaps between neighboring oriented regions. This method applies to any arbitrary angle, as well as, to images defined as an arbitrary number of bits per pixel.

I claim: 
     
       1. A method of rotating a digital image defined by a matrix of pixels A×B an angle φ where tangent φ=h/A wherein h is a number such that both A and B are divisable by h including the steps of: a. Dividing the image into blocks of size a×b where a=A/h and b=B/h;   b. Denote by i and j the columns and rows of a particular block with 0≦ij<A/h;   c. Displace the (i, j) block by i pixels in the vertical direction and by j pixels in the horizontal direction; wherein the improvement comprises the steps of:   d. Scaling down the original image by a factor proportioned to cosine φ; and   e. Making each block in the original image at least one pixel wider to overlap with a neighbor block.   
     
     
       2. The method of claim 1, including the steps of denoting by A and A1, respectively, the width of the original and of the rotated image and letting dA=A1-A. 
     
     
       3. The method of claim 2 including the step of eliminating dA columns and dA lines of pixels, obtaining the correct size when for every h/dA block moved, sB and sL are incremented respectively by an additional pixel and line, where sB points to the upper left corner of the source block and sL points to the source line of blocks. 
     
     
       4. A method of rotating a source digital images defined by a plurality of blocks, each block having a plurality of pixels p and being a pixels wide and b pixels high, into a destination digital imaged defined by a plurality of blocks, each of the images s and d, forming lines of blocks, comprising the steps of: a. Defining pointers sB, dB, sL, dL pointing, respectively, to the upper left corner of the source block, the destination block, the source line of blocks, and the destination line of blocks,   b. Moving the source line of blocks one at a time to the destination line of blocks and incrementing sB by a pixel and incrementing dB by a pixel, and decrementing sL and dL by one line,   c. Incrementing sL and dL by b lines and incrementing dL by one pixel after one line d blocks is rotated including the step of making the destination blocks a+1 pixels wide.